Volume of a Pyramid

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A pyramid is a solid closed geometric figure and is a 3-dimensional structure. There are different kinds of pyramids such as a pyramid with a square base or a rectangular base and every pyramid is surrounded by 4 triangles formed on the base. The base is connected by the triangles to the top most point of the pyramid known as the ‘apex’ or the ‘vertex’. Volume of the pyramid is the space contained inside the pyramid and is given as one-third times the product of the area of the base and the height.

Example 1: Calculate the volume of a square base pyramid whose base length is 4m and the height is 6m.

Given base length of the pyramid, b = 4m

Height of the pyramid, h = 6m

Volume of the pyramid, V = 1/3 * Area of the base * height

Area of the square base = b2 = (4m)2 = 16m2

Volume, V = 1/3 * 16m 2 * 6m = 32m3

Therefore, volume of the given pyramid, V = 32m3

Example 2: Calculate the volume of a rectangular base pyramid whose base length is 5m, width is 3m and the height is 7m.

Given base length of the pyramid, l = 5m

Width of the base, w = 3m

Height of the pyramid, h = 7m

Volume of the pyramid, V = 1/3 * Area of the base * height

Area of the rectangular base = length * width = 5m * 3m = 15m2

Volume, V = 1/3 * 15m 2 * 7m = 35m3

Therefore, volume of the given pyramid, V = 35m3